I had the same issue here, and fixed it using this: https://www.amazon.com/dp/B002ZPD07S?ref=ppx_pop_mob_ap_share. The outdoor box was larger then the hole, and this particular brand has a screw in the middle that keeps the receptacle together with the box when inserting plugs. No need to touch anything in the wall.

Edit: the product photo on Amazon is wrong. Google Intermatic wp1150c to see the correct picture. It comes with multiple inserts, the one for the duplex receptacle shows the screw hole I'm talking about.